One may think of a rational polyhedral cone \(\sigma \)  as a combinatorial analogue of an affine scheme and of \(S_\sigma \)  as its ring of functions. Quite like a scheme is glued from affine schemes, we may think of a rational polyhedral cone complex as a combinatorial object that is glued from rational polyhedral cones along their faces. Rational polyhedral cone complexes form a category that we denote by \(\mathbf {RPCC}\) . We refer the interested reader to [1]} for a precise definition of this notion. The category \(\mathbf {RPCC}\)  carries a natural Grothendieck topology that is generated by embeddings of rational polyhedral cones as faces, the face topology.
